A conventional fluorescent lamp assembly mainly includes a lamp set and a light bulb assembly. The light bulb assembly includes a shell, a socket and at least one lamp assembly. To install the light bulb assembly on the lamp set further requires a ballast and a starter to provide power to enable the light bulb assembly to function in a stable manner. The conventional fluorescent lamp assembly has the starter and ballast installed separately from the lamp set. The ballast is located at one side of the lamp set in a separated or integrated manner. In order to increase the application scope and operation efficiency, many fluorescent lamp assemblies at present adopt an improved structure to become a power-saving lamp (referring to FIG. 1). The power-saving lamp includes a lamp assembly 1, a socket 2, a shell 3, a connection element 8 and an electrode portion 6. There also is a housing space 4 spared between the socket 2 and shell 3. To improve power utilization efficiency each power-saving lamp has a power conversion element 5 which also provides the functions of the conventional starter and ballast. The power-saving lamp generally can be mounted onto a conductive socket by screwing like a conventional incandescent lamp to receive electric power. The power conversion element 5 transforms the electric power to generate light. The power-saving lamp provides a wider application scope and higher operation efficiency than the conventional fluorescent lamp. But it is more bulky than the conventional incandescent lamp due to housing the power conversion element 5. Lamp producers try to shrink the size of the power conversion element 5 to make the total size of the lamp set smaller. This makes driving multiple lamp sets 1 more difficult. Moreover, shrinking the size also increases energy density of the power conversion element 5, and the element materials of the power conversion element 5 must have a greater heat-resistant capability. All this make design of the power-saving lamp more difficult. As a result the power-saving lamp is more expensive than the general fluorescent lamp or incandescent lamp. There is still room for improvement to address the problems of design difficulty and higher cost mentioned above.